The difference between precious and semi-precious comes down purely to human definitions that have been imposed.

There is nothing in and of itself about the nature of a stone, which makes it precious or semi-precious.

Rather it is down to human desirability of an element or mineral or form or a stone that decides.

Generally, the rarer and more sought after a mineral is, the more likely it is to be defined as precious.

Desired, but more common and less valuable items may be, in contrast, semi-precious.